The classification of totally umbilical surfaces in homogeneous 3-manifolds
arXiv:1302.2876 · doi:10.1007/s00209-014-1381-8
Abstract
We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of totally umbilical surfaces in homogeneous Riemannian 3-manifolds.
21 pages